Final Eam Review MAC 1 Fall 011 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) (- + ) - = -( - 7) A) {- } B) {19} C) {- 9} D) {9} 1) Solve the equation b factoring. ) + - = 0 A) {1, } B) {-1, 1} C) {1, } D) {-1, } ) Find the -intercept(s) of the graph of the equation. Graph the equation. ) = + + ) - - A) -intercepts: -1 and - B) -intercepts: 1 and - - - - R1
C) -intercepts: 1 and D) -intercepts: -1 and - - - - - Add or subtract as indicated and write the result in standard form. ) i - ( - i) A) - i B) + i C) - i D) + i ) Solve the radical equation, and check all proposed solutions. ) + = + ) A) {-} B) {, } C) {} D) -, Solve the equation b making an appropriate substitution. ) - 1 + = 0 A) {, } B) {, 9} C) {-i, i, -i, i} D) {-,, -, } ) Solve the absolute value equation or indicate that the equation has no solution. 7) + + 9 = 11 1 A), B) {-, - 1 } C) -, - 1 D) 7) R
Solve the linear inequalit. Other than, use interval notation to epress the solution set and graph the solution set on a number line. ) - > - ) A) [-, ) -1-1 -11-9 -7 - - - - - -1 0 1 B) (-, -] -1-1 -11-9 -7 - - - - - -1 0 1 C) (-1, ) -1-0 -19-1 -17-1 -1-1 -1-1 -11-9 -7 D) (-, ) -1-1 -11-9 -7 - - - - - -1 0 1 Solve the absolute value inequalit. Other than, use interval notation to epress the solution set and graph the solution set on a number line. 9) + + 11 9) A) [-7, ] -1 - - - 0 B) (-, -7] [, ) C) (-7, ) -1 - - - 0 D) [-7, 11] -1 - - - 0-1 - - - 0 R
) + 1 - ) -9-7------1 0 1 7 9 A) (-, ] [, ) B) (-, -] [, ) -9-7------1 0 1 7 9 C) [, ] -9-7------1 0 1 7 9 D) [-, ] -9-7------1 0 1 7 9-9-7------1 0 1 7 9 Evaluate the function at the given value of the independent variable and simplif. 11) f() = - - ; f(-) A) -11 B) 1 C) - D) 11) Use the graph to determine the functionʹs domain and range. 1) 1) 1 - - - - - -1-1 1 - - - - - A) domain: (-, ) range: [-1, ) B) domain: [0, ) range: [0, ) C) domain: [0, ) range: (-, ) D) domain: [0, ) range: [-1, ) Graph the function. R
1) f() = + 1 if < 1 if 1 1) - - A) B) (1, ) (-1, ) (-1, ) (1, ) - - - - C) D) (-1, ) (1, ) (-1, ) (1, ) - - - - Use the given conditions to write an equation for the line in slope -intercept form. 1) Passing through (, ) and (7, ) A) - = - ( - ) B) = - + C) = + D) = m + 1) R
Graph the line whose equation is given. 1) = - - 1 1) 1 - - - - - -1 1 - - - - - A) B) 1 1 - - - - - -1 1 - - - - - - - - - - -1 1 - - - - - C) D) 1 1 - - - - - -1 1 - - - - - - - - - - -1 1 - - - - - Use the given conditions to write an equation for the line in the indicated form. 1) Passing through (, ) and perpendicular to the line whose equation is = + 7; point-slope form 1) A) - = 1 ( - ) B) - = 1 ( + ) C) = - - 11 D) - = - 1 ( - ) R
Begin b graphing the standard quadratic function f() =. Then use transformations of this graph to graph the given function. 17) h() = ( - 7) - 17) - - - - - - A) B) - - - - - - - - - - - - C) D) - - - - - - - - - - - - R7
Begin b graphing the standard absolute value function f() =. Then use transformations of this graph to graph the given function. 1) g() = 1 + + 1) - - - - - - A) B) - - - - - - - - - - - - C) D) - - - - - - - - - - - - R
Begin b graphing the standard cubic function f() =. Then use transformations of this graph to graph the given function. 19) g() = -( - ) + 19) - - - - - - A) B) - - - - - - - - - - - - C) D) - - - - - - - - - - - - Find the domain of the function. 0) - 9 0) A) (-, ) B) (9, ) C) [9, ) D) (-, 9) (9, ) For the given functions f and g, find the indicated composition. 1) f() = + +, g() = - (g f)() 1) A) + + B) + + C) + + D) + + R9
Find the inverse of the one-to-one function. ) f() = - 7 ) A) f-1() = + 7 B) f-1() = + 7 C) f-1() = - 7 D) f-1() = - 7 Write the standard form of the equation of the circle with the given center and radius. ) (-, ); A) ( - ) + ( + ) = 9 B) ( - ) + ( + ) = C) ( + ) + ( - ) = D) ( + ) + ( - ) = 9 ) Determine whether the given quadratic function has a minimum value or maimum value. Then find the coordinates of the minimum or maimum point. ) f() = - - - A) minimum; -, - 1 B) maimum; - 1, - C) maimum; -, - 1 D) minimum; - 1, - ) Find the domain of the rational function. ) f() = + - ) A) { -,, } B) all real numbers C) { -, } D) { 0, } Find the vertical asmptotes, if an, of the graph of the rational function. - 1 ) g() = ( + ) ) A) = - B) = 1 and = - C) = 0 and = - D) no vertical asmptote + 7) h() = - 1 7) A) =, = - B) = - C) = D) no vertical asmptote Find the horizontal asmptote, if an, of the graph of the rational function. 1 ) f() = + 1 ) A) = 1 B) = C) = 0 D) no horizontal asmptote R
Solve the polnomial inequalit and graph the solution set on a number line. Epress the solution set in interval notation. 9) + - 9) -9-7 - - - - - -1 0 1 7 9 A) [-, -1] B) [1, ] -9-7 - - - - - -1 0 1 7 9-9 -7 - - - - - -1 0 1 7 9 C) (-, 1] [, ) D) (1, ) -9-7 - - - - - -1 0 1 7 9-9 -7 - - - - - -1 0 1 7 9 Solve the rational inequalit and graph the solution set on a real number line. Epress the solution set in interval notation. 0) + 0) -9-7------1 0 1 7 9 A) (-, -) or [0, ) B) (-, ] -9-7------1 0 1 7 9 C) [-, -) -9-7------1 0 1 7 9 D) (-, -] or (-, ) -9-7------1 0 1 7 9-9-7------1 0 1 7 9 Write the equation in its equivalent eponential form. 1) log b 9 = 1) A) b = 9 B) 9 = b C) b = 9 D) 9b = Write the equation in its equivalent logarithmic form. ) 1 = 1 A) log 1 = 1 B) log 1 1 = C) log 1 1 = D) log 1 = 1 ) R11
Evaluate the epression without using a calculator. ) log 1 ) A) B) C) 1 D) 1 Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. ) log - ( + ) ) A) log + log + log ( - )1/ - log - log ( + ) B) log ( - ) - log (( + )) C) log + log + 1 log ( - ) - log + log ( + ) D) log + log + 1 log ( - ) - log - log ( + ) Solve the equation b epressing each side as a power of the same base and then equating eponents. ) 1 + = - A) {1} B) {} C) {1} D) {9} ) Solve the logarithmic equation. Be sure to reject an value that is not in the domain of the original logarithmic epressions. Give the eact answer. ) log 1 ( + ) = 1 - log 1 ) A) {-} B) {-} C) {} D) {} Solve the sstem of equations. 7) - + z = + + z = + - z = - 7) A) {(-,, 1)} B) {(, 1, -)} C) {(1, -, )} D) {(1,, -)} Evaluate the determinant. ) -1 A) B) C) D) -7 ) Use Cramerʹs rule to solve the sstem. 9) = - + = - - 1 9) A) {(-, -)} B) {(, -)} C) {(-, )} D) {(-, -)} R1
Evaluate the determinant. 0) 1 A) 9 B) -1 C) D) 0) R1
Answer Ke Testname: FINAL_EXAM_REVIEW 1) C ) D ) D ) B ) C ) D 7) C ) D 9) A ) B 11) C 1) D 1) A 1) B 1) A 1) D 17) C 1) D 19) B 0) B 1) B ) A ) D ) B ) C ) C 7) C ) C 9) A 0) C 1) C ) C ) D ) D ) B ) C 7) C ) C 9) C 0) C R1